(1 po
3. Your cell phone plan is $35.98/month plus a utilities tax of 6.5% APR. During the year, you go
40 minutes over your plan at a rate of $0.35/minute. How much do you pay for the overages?

Answer:

-243

Step-by-step explanation:

x^5 = x * x * x * x * x

( - 3 )^5 = (-3) * (-3) * (-3) * (-3) * (-3) = -243

The ordered pair in roaster form {(2,8), (3, 12), (4, 16), (5, 20)} is a function.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

We know a function can be many one which means different inputs leads to same output but one to many is not a function as same input can not lead to different outputs.

{(2,8), (3, 12), (4, 16), (5, 20)} is a function as each different input leads to a different output.

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Given O is the midpoint of PT and RS

Therefore, In triangles POR and TOS, we have

PO = TO (O, the midpoint of PT);

∠POR=∠TOS, (vertically opposite angles);

RO=OS, (O, the midpoint of RS)

So by SAS postulate, we have

△POR = △TOS    Hence proved

What is the midpoint?

The midpoint is a line segment's center point in geometry. The midpoint is also the centroid of the segment and the endpoints are equally spaced from both endpoints. The midpoint can also be described as a point that divides a segment in half or as one that is equally spaced from both ends of a line.

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Answer:

X=5

Angle c is 42 degrees

Step-by-step explanation:

sum of all angles in a triangle equal 180 degrees so we set all these angles equal to that

(9x-3)+(22x+1)+(42-3x)=180

31x-2+42-3x=180

28x+40=180

      -40.  -40

28x=140

/28.   /28

x=5

So now to find angle c we just fill in X

9(5)-3

45-3

42

Hopes this helps please mark beainliest

Using local linearity, f(1.2) = 9.46

Local linearity is the aprroximation of a curve at a point into a linear function.

For a locally linearized function f(x) about a point x'

f(x + Δx) = f(x) + f'(x)Δx

Now, since we desire to use local linearity to estimate f(1.2)

f(1.2) = f(1 + 0.2)

So, we have that comparing the with f(x + Δx) above, we have

f(1 + 0.2) = f(1) + f'(1)(0.2)

Given that

Substituting the values of the variables into the equation, we have

f(1 + 0.2) = f(1) + f'(1)(0.2)

f(1 + 0.2) = 9.4 + (0.3)(0.2)

f(1 + 0.2) = 9.4 + 0.06

f(1 + 0.2) = 9.46

f(1.2) = 9.46

So, f(1.2) = 9.46

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The slope-intercept representation of the linear function that passes through the points (-1, 10) and (5, -8) is:

y = -3x + 7.

The slope-intercept representation of a linear function is presented by the equation shown as follows:

y = mx + b

The coefficients of the function, along with their meaning, are presented as follows:

The two points that belong to the linear function are given as follows:

(-1, 10) and (5,-8).

Given two points, the slope is calculated as the change in y divided by the change in x of the points, hence:

m = (-8 - 10)/(5 - (-1)) = -18/6 = -3.

Then the format of the equation is:

y = -3x + b.

When x = -1, y = 10, hence the y-intercept of the function is obtained as follows:

10 = -3(-1) + b

10 = 3 + b

b = 10 - 3

b = 7.

Hence the equation is:

y = -3x + 7.

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Answer:

$1,078

Step-by-step explanation:

The tax amount is taken out of his taxable income,

The tax amount is $1583.

A tax is a mandatory contribution that a local, regional, or national government collects from individuals or businesses. Public works and services like roads and schools, as well as programs like Social Security and Medicare, are financed by tax revenue.

In economics, taxes go to whoever has to pay them, whether it's the entity being taxed, like a business, or the people who buy the goods from the business. Payroll taxes, federal and state income taxes, and sales taxes are just a few of the taxes to take into account from an accounting perspective.

Given

adjusted gross income = $26,045

exemption =  $12,400

to find tax by  taxable income

 taxable income =  adjusted gross income - exemption

taxable income =  26,045 - 12400

taxable income = $13,645

The question is incomplete, the table is attached

Therefore, I will employ the 2016 single taxable income tax bracket and rate table.

Using the table, the tax amount on an income of $13,645 is:

Tax = $927.50 + 15% × (Amount - $9275)

So, we get:

Tax = $927.50 + 15% ×($13645 - $9275)

$1583,

Hence, Allie's tax amount is $1583.

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The table for Question is in image attached.

The factors are (x-1) (8x²+1).

What is a factor?

A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.

For example, 3 and 8 are factors of 24 because 24 ÷ 3 = 8 exactly and 24 ÷ 8 = 3 exactly. The other factors of 24 are 12, 4,6

8x³-8x²+x-1

Take out 8x² as common

8x² ( x-1) + (x-1)

Take out (x-1) as common

(x-1) (8x²+1)

So, the factors are (x-1) (8x²+1).

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Answer:

I think it 3 or 2 but mainly 2

The value of 54% as a fraction is 27/50.

The value of 0.22 as a fraction is 11/50.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case 54% will be:

= 54 / 100

= 27 / 50

Also, the value of 0.22 will be:

= 22 / 100

= 11 / 50

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$7969.24 invested at 8% and $3930.76 invested at 5%

From given information,

Amount invested = $11,900

Rate of interest for first part = 8%

Rate of interest for second part = 5%

Let the amount invested for 8% be 'x'.

Let the amount invested for 5% be 'y'

According to question, we get an equation,

0.08x - 0.05y = 441

x + y = 11,900

x = 11,900 - y

0.08(11,900 - y) - 0.05y = 441

952 - 0.08y - 0.05y = 441

-0.13y = -511

y = (-511)/(-0.13)

y = 3930.76

so, x = 11,900 - 3930.77

x = 7969.23

Therefore, $7969.24 invested at 8% and $3930.76 invested at 5%

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Try this option ↓

Step-by-step explanation:

1) if to evaluate the given limits using math methods, then:

[tex]\lim_{h \to 0} \frac{2.7^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.7^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.7^h*ln2.7}{1} =ln2.7;[/tex]

and

[tex]\lim_{h \to 0} \frac{2.8^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.8^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.8^h*ln2.8}{1} =ln2.8;[/tex]

2) for more info see the attached graphs; note, ln2.7≈0.993252, ln2.8≈1.029619 and the function is undefined in the points where x=0.

Using A as the center of dilation and a scale factor, BC is dilated by 12 units.

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Answer:

The Graph On Letter C

Step-by-step explanation:

It's going at a rate of change/slope of -5/2.

260 occurrences of the letter e we can expect to find.

Frequency = 13%

Total letters = 2000

E letters = 13% of 2000

              = (13/100)*2000

              = 13*20

              = 260

Hence, there are 260 e letters in 2000 of total letters.

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Answer:

20%.

Step-by-step explanation:

A sum of money will triple itself in ten years at an annual interest rate of 20%.

The diameter of  the boulder assuming a sphere. is 38m

Specific gravity is defined as density of a substance to the density of water

SG = density of boulder/ density of water

Since (at standard temperature and pressure) water has a density of 1

SG =  mass of boulder / volume of boulder

2.6 = 560 x 1000/ x

x = 56000/2.7

x = 20740.74

The volume of a sphere = 4/3 πr³ =

20740.74 = 4/3 (3.14) r³

r³ = 4953

r = 17.04

Diameter = 2r = 2x17.04 = 38.08

Therefore, the diameter of  the boulder assuming a sphere. is 38m

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=-2 \end{cases}\implies y=a(x-3)^2 -2\hspace{5em}\textit{we also know that} \begin{cases} x=1\\ y=2 \end{cases} \\\\\\ 2=a(1-3)^2 -2\implies 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a \\\\[-0.35em] ~\dotfill\\\\ y=1(x-3)^2 -2\implies {\Large \begin{array}{llll} y=(x-3)^2 -2 \end{array}}[/tex]

Answer:

∴ x = 0.707 (to 3sf)

Step-by-step explanation:

Following the Pythagoras' Theorem,

  1² = x² + x²

2x² = 1

 x² = [tex]\frac{1}{2}[/tex]

∴ x = 0.707 (to 3sf)

The equation of the graph g(x)  is [tex]3^{x-6}[/tex]

What is a graph ?

A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;

In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.

The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

If the graph of the function  f(x) = 3^x is translated 6 units to the right , then the function becomes

g(x) = f(x - 6)

     = [tex]3^{x-6}[/tex]

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Answer:

her total cost is $29.45

Step-by-step explanation:

last week - 8 1/2 gallons times $2.30 = $19.55

this week - 4 1/2 gallons times $2.20 = $9.90

$19.55 + $9.90 = $29.45

Properties used for each steps are Division property, Multiplication property, Addition property, Subtraction property and Distributive property.

Given equation is {2(2/5 x + 8)}/2 = {4(14- 1/5 x)}/2

1) Here first we used Division property

we divide both the equation by 2 then the equation become

(2/5 x + 8) = 2(14-1/5 x).

2) Now we will use Multiplication property,

2/5 x + 8 = 28 - 2/5 x

Interchanging the terms we get

2/5 x + 2/5 x = 28-8

3) By Addition property

4/5 x = 28-8

4) And by Subtraction property we get

4/5 x = 20

5) Lastly by Distributive property we find the value of x,

x = (20 × 5)/4

x = 100/4

x = 25

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Answer:

f(x)=4x^2 is facing up, it has a minimum, and it's horizontally compressed

Step-by-step explanation:

It's facing up because there's no negative sign in front of the coefficient of x.

It has a minimum because any quadratic function that faces up will have a minimum, and any quadratic function that faces down will have a maximum.

It's horizontally compressed because as can be seen in the picture below, f(x)=4x^2 (red) has more "slope," so it's condensed toward the y-axis. Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed, and if the coefficient is smaller than 1, then the function will be horizontally stretched.

The cost per message is $0.025 and  the graph that represents the Jerry's text message plan is graph 2

The cost of every 30 messages = $0.75

To find the cost of one message we have to use the unitary method

The cost of 1 message = The cost of every 30 messages / 30

Substitute the values in the equation

The cost per message = 0.75 / 30

Divide the terms

= $0.025

Next find the cost 40 messages = The cost per message × 40

Substitute the values in the equation

The cost of 40 messages = 0.025 × 40

= 1

Using these details the graph that represents the Jerry's text message plan is graph 2

Hence, the cost per message is $0.025 and  the graph that represents the Jerry's text message plan is graph 2

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Answer:

-7/6

Step-by-step explanation:

You can get the slope of the line that passes between two points by taking the difference of the y values and dividing that by the difference of the x values:

[tex]\frac{12-5}{2-8} =\frac{7}{-6} =-\frac{7}{6}[/tex]

The expression that is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100) is 2(3x² + 1x + 104)

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

This will be illustrated as:

2(3x^2-6x+4)+2(-2x+25x+100)

= 6x² - 12x + 8 - 4x + 50x + 200

= 6x² +34x + 208

= 2(3x² + 1x + 104)

The equivalent expression is 2(3x² + 1x + 104).

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Answer:

b = 65°

Step-by-step explanation:

Now we have to,

→ find the required value of b.

Forming the equation,

→ 115° + b = 180°

Then the value of angle b is,

→ 115° + b = 180°

→ b = 180° - 115°

→ [ b = 65° ]

Hence, the value of b is 65°.

If the function over the interval 3 ≤ x ≤ 4 then, the average rate of change, in simplest form, is 9.

What is average rate of change?

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

m = dy/dx

m =y₂ - y₁ / x₂-x₁

The function over the interval 3 ≤ x ≤ 4.

Using the coordinate points from the table (3, 31) and (4, 22)

Here, y₂ = 22, y₁ = 31 , x₂= 4, x₁ = 3.

Substitute the coordinate into the expression:

= 22 - 31 / 4 - 3

= 9 / 1

m = 9

Hence, the function over the interval 3 ≤ x ≤ 4 ;  the average rate of change is 9.

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